AC Resistance of a Conductor

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A conductor offers a greater resistance to the flow of alternating current(AC) than it does to direct current(DC). The magnitude of the increase is usually expressed as an “AC/DC ” ratio. The reasons for the increase include:
  1. Skin effect, 
  2. Proximity effect, 
  3. Hysteresis and eddy current losses in nearby ferromagnetic materials, and
  4. Induced losses in short-circuited nearby non-ferromagnetic materials
Skin Effect
Skin Effect describes the phenomena of alternating current flowing more densely near the surface of a conductor. The net effect is a reduction in effective area and an increase in the resistance. To calculate skin effect in tubular conductors made of solid wire to an infinitely thin tube, the curves of Ewan are used.
The parameter is:
The table below gives the factors for skin effect ratio R/R0 as a function of X, where R is the AC resistance and R0 is the DC resistance. Note that from the table, R/R0 is the resistance ratio due to skin effect. L/L0 is the inductance ratio due to skin effect. X is as defined by the formula above.

For conductors larger than 1,500,000 circular mils,other calculation formulas must be used for accuracy. The non-uniform cross-sectional distribution of current also affects the inductance, the value of which is less than if the current density were uniform. The table of skin effect ratios above, therefore, lists the inductance ratio L/L0 where L is the inductance due to a non-uniform current density and L0 is the inductance assuming uniform current density.

Proximity Effect:
Proximity effect is the distortion of the cross-sectional current distribution of the conductor due to nearby currents. To calculate approximately the proximity effect, use the following formula:
Where:
fp       = The factor to account for proximity effect
GMR = The geometric mean radius of the equal conductors
GMD = Geometric mean spacing of the conductors
R/R0  = Skin effect ratio

After determining skin and proximity effect, the effective resistance of a conductor taking these two factors into effect is then given by:
Where:
R/R0 = Skin effect ratio
fp      = Factor accounting for proximity effect